Re: Little(?) problem: What is the formula ???

*To*: mathgroup at smc.vnet.net*Subject*: [mg21948] Re: [mg21911] Little(?) problem: What is the formula ???*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 5 Feb 2000 00:49:21 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

>Hello All ! > >I have two "series" of data : >The first serie are "normal values" >The seccond serie represents a percentage(Value) of an amount(Nominator) > >Serie 1) >Value Nominator >100 1 >150 1 >125 1 > > >Serie 2) >Value Nominator >10 100 >12 200 >15 300 > >The Problem: >-------------------------------------------------------------------------- >I want to find a GENERAL formula to calculate the SUM of these series, >So a formula which gives the following results > >Serie 1) 365 >Serie 2) 13,1 > > >Explanation results: >Serie 1) 100+150+125 = 375 > >serie 2) 10% of 100 = 10 > 12% of 200 = 24 > 15% of 300 = 45 >So total amount = 600 and the fraction=79 so that is 13.1% > > > >What is the general formula (using value and nominator) ????????? > > >Thank you very much !!! > I am assuming that you are rather new to Mathematica and want to know how to do this using Mathematica methods. So I will do the steps in some detail. Let's take the first sum first. We would represent the series in Mathematica this way: series1 = {{100, 1}, {150, 1}, {125, 1}} {{100, 1}, {150, 1}, {125, 1}} I will assume that the 1's are weighting factors and may be something other than 1. (This will help us in evaluating the second series.) So the first thing we want to do is multiply the items in each inner List. We can do that by changing the List to a Times by using the Apply statement and mapping it onto each of the inner Lists. Apply[Times, #] & /@ series1 {100, 150, 125} Then to convert this List into a sum we Apply Plus to the above output. Plus @@ {100, 150, 125} 375 Here we set up a single expression which will work for any series of the series1 type. Plus @@ (Apply[Times, #] & /@ series1) 375 If you are new to Mathematica you will want to study Map (also sometimes denoted by /@ ), Apply (also sometimes denoted by @@ ) and also pure functions in Help. Now for your second type of series. series2 = {{10, 100}, {12, 200}, {15, 300}}; The numerator of your expression is just going to be what is produced by your first type of sum. We could divide by 100 to get 79, but since you want percent we would just have to multiply by 100 when we finished. Plus @@ (Apply[Times, #] & /@ series1) 7900 For the denominator we just want the sum of the second elements in each list. The easiest method to do this is probably just to sum the lists, by Applying Plus Plus @@ series2 {37, 600} and then taking the last part. Last[{37, 600}] 600 So now we can combine the numerator and denominator, and since we want a real number and not a fraction, use N on the result. N[Plus @@ (Apply[Times, #] & /@ series2)/Last[Plus @@ series2]] 13.1667 Finally, if you are going to do many of these sums you can define functions to evaluate them. sumtype1[series_] := Plus @@ (Apply[Times, #] & /@ series) sumtype2[series_] := N[sumtype1[series]/Last[Plus @@ series]] sumtype1[series1] 375 sumtype2[series2] 13.1667 David Park djmp at earthlink.net http://home.earthlink.net/~djmp/

**Re: Little(?) problem: What is the formula ???**

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**Re: Little(?) problem: What is the formula ???**

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